On super restricted edge-connectivity of edge-transitive graphs

Let X = ( V , E ) be a connected graph. Then X is called super restricted edge-connected, in short, sup- λ ′ , if every minimum edge set F of X such that X − F is disconnected and every component of X − F has at least two vertices, the set of edges being adjacent to a certain edge with minimum edge degree in X . In this paper, by studying the λ ′ -superatoms of X , we characterize super restricted edge-connected edge-transitive graphs. As a corollary, we present a sufficient and necessary condition for connected vertex-transitive line graphs to be super vertex-connected.